Interesting… So in my last entry I wrote on & on about lines of symmetry, and after looking at this rendering a bit more, I think some of my analysis was partially incorrect. Lemme break it down…

Okay so this map should fall in line with what I was saying comprises a 2 seam map, but what I found is another two lines of symmetry- lines that all 2 seamed maps contain is actually 4 lines of symmetry. In constructing this map I used a total of 4 infinite planes with each in groups of 2. The first two are 75 X 75 in size and at a Z angle of 5 & -5 respectively, and the second two are 75 X 75, at an angle of Z angle of 5 & -5, but rotate 90 degrees. In a 3D space this create a wedge of sorts.

To mentally picture this, imagine each pair as an X (each plane is at +-5 degrees), but instead of looking at the X from above, as you are now looking at the character on the screen, imagine that you are only looking at one side, which makes the X look more like a V. Furthermore, you are looking at the V from the side looking down into the vertex of the V, so you see two sides and at the apex is the central seam. By rotating the second pair 90 degrees, the V turns into a pyramid with 4 sides, and you are looking at the pyramid from below it’s base. Thus you get 4 different lines of symmetry for each seam. This make sense? I can take some screen shots to explain this a bit more…

With this jargon out of the way, the result is that with two grouped planes, I get 4 lines of symmetry. And it can be assumed that with 3 grouped planes, I get 6 lines of symmetry and so on. I think the most effective way to classify all the maps in the quilt project will be based of lines of symmetry (aka seams) because these can easily be identified, while the number of infinite planes (which result in the number of seams) is not as easily identifiable.

With #40 out of the way, its time to go through and classify them all……..fun!
==Update==
I ended up using the geometry as the means categorize my maps.

Like Providence, I have yet to visit downtown Houston, however I can still manipulate the city to some degree. Today’s degree is to the tune of about 60 :-) 360 divided by 60 equals 6 (which equals 3 lines of symmetry which I call “seams” of the quilt) and judging by my last quilts, I’ve found this number to be my favorite degree of manipulation.

So far I’ve made about 39 different quilts (multi-planar maps), and I think it is about time to begin the subdivision of the quilt project into the number seams each quilt has. This means I have to create a sub-category for each number of seams, and then go back through every blog entry and assign each quilt to it’s respective category. This will allow a casual visitor to this site the ability to look at all of the quilts at once or by each respective number of seams.

Starting at 2 seams, like the Ivan Memory (the first quilt) and Beverly Hills Quilt #3, then to 3 seams, like today’s quilt, and then quilts that have greater than 4 seams. This categorization of the quilt project will be helpful in the long run because it will show the ways the geographic tessellations react when reflected multiple times and more importantly it will help organize what has been my favorite projection of 2005.

As for Houston Quilt, the imagery is from 2002 from the USGS (of course!) and I modified the imagery in such a way that the center of the tessellation is Highway 45 and the high-rise buildings of downtown Houston surround it.

The drawback of this imagery, similar to my Denver imagery, is that the aerial photograph was taken in the afternoon and due to the angle of illumination, the shadows obscure much of the ground. Yet this can also be a nice aspect too because the shadows also reflect and make the rendering special in their own way.

I’d rather have the photograph taken from nadir (straight above) at noon on cloudless, sunny day (this eliminates shadows and distortion at the center of the scene). But of course that would be too easy right? :-)

The other drawback is that the imagery itself is somewhat devoid of colors. Granted the sensors did pick up colors, but they are not very vibrant. When looking at the map above it almost appears to be black & white, but when you look at the details you can see some color.

Maybe I should go in and modify the imagery again and add color? In the past, the closest I’ve gotten to doing that was embedding my name into the imagery, and that wasn’t that special. The Boston imagery is still some of my favorite imagery because of the color variations and the good news it that I also downloaded imagery of downtown Houston from 2004 which has an interesting patch of different colored imagery in. When tessellated, this imagery will add that colorful dimension this map currently lacks. First I have to prepare the imagery and I think I might just make another map using the Houston imagery. I was thinking of maybe a 2 seamed map or should it be 4? I’ll find out soon!

==Update==
I ultimately used the geometric shape instead of the lines of symmetry for my naming convention.

Nikolas Schiller is a second-class American citizen living in America's last colony, Washington, DC. This blog is my on-line repository of what I have created or found on-line since May of 2004. If you have any questions or comments, please contact:If you would like to use content found here, please consult my Fair Use page.